Finite-SNR Diversity-Multiplexing Trade-Off of Dual Hop Multiple-Relay Channels

This paper investigates the finite signal-to-noise ratio (SNR) diversity-multiplexing trade-off (DMT) of point-to-point wireless channels assisted by multiple relays. Results are derived for both amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. For the AF protocol, we derive accurate approximations for the system outage probability when the relays are clustered between the source and destination. For the case where all the relays are clustered near the destination, an exact closed-form expression for the system outage probability is obtained. For the DF protocol, under general multiple relaying configurations, we derive an exact closed-form expression for the system outage probability. The outage results for AF and DF are used subsequently to yield expressions for the finite-SNR DMT. We also extract the conventional asymptotic DMTs as special cases of the finite-SNR results, and demonstrate that the asymptotic DMTs can significantly overestimate the level of diversity that is achievable for practical error rates and SNRs.